Recall that a 2-flag complex is a complex \(\Delta \)  such that each minimal nonface of
\(\Delta \)  has cardinality 2. Recall that a complex is a 2-flag complex if and only if \(\Delta \) 
is a clique complex of a graph ([1]}). Note
that the Alexander dual \(\Delta ^\vee \)  of a 2-flag complex is pure of dimension \(|V(\Delta )|-2\) .
